What is the solution to the inequality #2 <2(x+4)<18#?

1 Answer
Aug 30, 2015

Answer:

#-3 < x < 5#

Explanation:

Given
#color(white)("XXXX")2 < 2(x+4) < 18#
#rArrcolor(white)("XXXXXXXXXXXXXXX") 2 < 2x+8 <18#

Things you can do with expressions in an inequality which maintain the inequality:

  • Add the same amount to each expression
  • Subtract the same amount from each expression
  • Divide each expression by the same amount provided the amount is greater than zero
  • Multiply each expression by the same amount provided the amount is greater than zero

#2 < 2(x+4) < 18color(white)("XXX")rArrcolor(white)("XXX") 2 < 2x+8 <18#

Given the above rules, we can subtract #8# from each expression, to get:
#color(white)("XXXX")-6 < 2x < 10#

Then we can divide each expression by #2#, to get:
#color(white)("XXXX")-3 < x < 5#